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PINAKI SANKAR RAY, M.Sc. (CALCUTTA)

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PINAKI SANKAR RAY, M.Sc. (CALCUTTA) THEORY OF ABSORFHON OF HIGH ENERGY (MeV-GeV) NUCLEI AND OF REHEAT FOR THERMONUCLEAR REACTIONS IN INERTIALLY CONFINED LASER COMPRESSED PLASMA PINAKI SANKAR RAY, M.Sc. (CALCUTTA) THESIS SUBMITTED FOR THE DEGREE OF DOCTOR of PHILOSOPHY IN THE FACULTY OF SCIENCE THE UNIVERSITY OF NEW SOUTH WALES AUGUST 1977 y 'IVERSITY OF N.S.W. 43303 2VAPR.78 LIBRARY riiwy1^ mm'**** (i) ACKNOWLEDGEMENT The author is deeply indebted to Professor Heinrich Hora, Head of the Department of Theoretical Physics, for suggesting the problem and supervising the research. He has introduced him to the subject of laser fusion, and above all his enthusiasm for work has been the author's greatest encouragement. (ii) ABSTRACT The theory of laser induced nuclear fusion reactions under inertial confinement has been investigated in this work. The special reactions treated numerically are the deuterium-tritium and the hydrogen-boron(11) fusion in plasma of densities corresponding to the solid state and higher. The energy gain has been calculated both with and without the incorporation of plasma heating due to the absorption of the MeV alphas released in the reactions. This reheat by the alphas is related to their range and the concept of the penetration length of energetic charged particles in plasma has been discussed from the point of view of the Fokker-Planck formalism. As a point of theoretical interest the process of soft photon emission during scattering as necessitated by quantum electrodynamics has also been incorporated in the Fokker-Planck method. In this case one does not need the Coulomb logarithm to avoid the divergence of small angle scattering. However there arises another term due to quantum electrodynamic cut-off. A new model called the "collective model" has been constructed for the calculation of the range of high energy charged particles in high density plasma. This (iii) model is very close to the Bethe-Bloch type theory in use in nuclear physics and Bagge's modification of it for the penetration of high energy electrons in plasma. This calculation differs essentially from the Fokker-Planck theory for high density hot plasma — it predicts range for particles of MeV initial energy shorter by a factor of 1000 in some cases. Furthermore the range decreases with the rise of plasma temperature in contrast to the Fokker-Planck calculations. It is also suggested that the collective model should be applied for the study of heavy-ion injection in plasma and some numerical results of uranium range are illustrated. For the calculation of fusion efficiency the cooling of the plasma due to adiabatic expansion has been taken into account. The break even energies of DT and HB11 for solid state density are found to be 1.5x106 J and 2.5xl013 J respectively without the incorporation of reheat. Then it has been shown how to introduce the reheat mechanism together with ionic depletion. In this case the equations governing the thermokinetic expansion can only be treated numerically due to complexity. The influence of reheat is noted only at higher densities — for the solid state density it is negligible. One significant aspect of this addition of reheat is the ignition. This can be defined as the optimised stage where, although the initial temperature of the fuel is relatively low, the absorption of hot alphas produced by the few initial reactions is strong enough to offset the (iv) temperature drop due to inertial expansion so that the temperature gets raised to a point where the reaction cross -section is large. This occurs only at high densities, e.g., for DT plasma of initial density 103 times the solid state and initial temperature 2 keV with initial volume 10 cm3 one would obtain a gain of 210 for input laser energy of 6 kJ. For HB11 plasma with initial density 105 times the solid state density — which is theoretically possible under the concept of nonlinear force mechanism as developed by Hora — and temperature 22 keV and volume 10 -8 cm ^ a gain of 22 is reached for input energy of 2 MJ. CONTENTS Acknowledgement (i) Ab s t r a c t (ii) List of Publications (v) Chapter I Introduction 1 Chapter II Resume of cross-sections of nuclear reactions 6 Chap ter III Models of the range of energetic charged heavy particles in plasma 19 3.1 The Fokker-Planck formalism 20 3.2 Energy loss in Fokker-Planck formalism 27 3.3 Coulomb Interaction 31 3.4 Scattering with soft photon emission 36 3.5 The collective model for energy loss 44 3.6 Relation to the Bethe-Bloch formalism and Bagge's modification ^9 3.7 Numerical discussions and conclusions 55 Chapter IV Introduction 64 4.1 Model of a high density expanding plasma 65 4.2 Mathematical formulation of the Thermo- kinetic expansion theory 67 4.3 .Fusion yield in adiabatica1ly expanding plasma ^0 4.4 Contribution from alpha particle reheat 73 4.5 Numerical results and discussions 80 Chapter V Heavy Ion Penetration 101 Conclusion 109 Appendix I 1 1 1 Appendix II 113 Appendix III 115 Ref erences 119 Computer Program 125 Photocopies of Publications 129 (v) LIST OF PUBLICATIONS H. Hora and P.S. Ray: Bull. Am. Phys. Soc. , 2_1, 73 , (1976) "Reaction Gain of Hydrogen-Boron (11) at Laser Compressed Plasmas". P.S. Ray and H. Hora: Nuclear Fusion, 16 , No.3 , 535-36 ( 1976) "On the range of alpha particles in laser produced superdense plasma". P.S. Ray and H. Hora: At omkernenergie, 2j8, No. 3 , 15 5-157 ( 1976) "Penetration Length of Alpha particles at Laser- produced Thermonuclear reactions". P.S. Ray and H. Hora: Bull. Am. Phys. Soc., 21, 1153 (1976) "Thermalization Length of Alphas and other Nuclear particles in High Temperature Plasmas". P.S. Ray and H. Hora: Zeit. f. Naturforschung, 3 2A, 538-543 (1977) "On the Thermalisation of Energetic charged particles in Fusion plasma with Quantum E1ectrodynamic considerations". R. Castillo et al: Nuclear Methods and Instruments, 144 , 2 7-32 , (197 7) "Advanced Fuel Nuclear Reaction Feasibility Using Laser Compression II". P.S. Ray and H. Hora: Laser Interaction and Related Plasma Phenomena, eds. H.J. Schwarz and H. Hora, Vol.4B, p 1081-1102, Plenum (N.Y.), 1977 "Corrected penetration Length of Alphas for Reheat Calculations". H. Hora and P.S. Ray: Atomkernenergie, 30 , 261 (197 7 ) "Ueber die elektrostatische Bindungsenergie von Plasma und ihr Zusammenhang mit E1ementarkonstanten". 1 CHAPTER I INTRODUCTION: This thesis encompasses investigations on the theory of energy release by nuclear fusion and some problems related to it. Fusion denotes nuclear reaction processes in which lighter nuclei combine under nuclear forces to form heavier nuclei but where the mass differences involved imply the release of enormous energy. Under the present understanding of physics there exists in nature four categories of forces or interactions, namely gravitation, weak interactions, electromagnetic and strong nuclear forces. The last mentioned is the least understood of these at least from a theoretical point of view although in recent years there has been a great accumulation of experimental results. The nuclear forces are of very short range and are attractive at first then becoming repulsive at very short distances. The attractive part is respon­ sible for the binding of the nuclei of elements which are constituted of protons and neutrons. The strength of these forces are much greater than the electromagnetic forces whereas the range as mentioned earlier much less 2 e.g. almost zero for atomic distances. Thus in order that fusion should take place the respective nuclei should be close enough. In the normal state of matter this is prevented by the repulsive electric forces between different nuclei due to their positive electric charges. One of the main problems for a successful fusion reaction to perform is therefore that of overcoming this repulsion. Now every nucleus is characterised by two fundamental integers A the mass number and Z the number of protons in it which defines its charge apart from other quantum numbers as spin etc. If N be the number of neutrons in the nucleus one has A = Z + N. For stable nuclei Z - N - . Thus the heavier the nuclei the electric repulsion between them is higher. One has therefore almost always considered the feasibility of fusion with different isotopes of hydrogen for example the deuterium-deuterium^ reaction which proceeds in two ways D + D -+ He3 + n D + D -* T3 + p Although fusion reactions can be achieved in the laboratory by bombarding a target with energetic nuclear projectiles obtained with the help of accelerators one cannot realise a sustained reaction in this way which is necessary for successful energy production - in a cold target the electrons will absorb most of the energy of the incident projectiles. The only method available at present for this is to raise the temperature of the nuclear fuel so 3 high that the random thermal motion enable the nuclei to overcome the Coulomb repulsion and thus initiate fusion. At this high temperature matter is always in the plasma state and this is the main reason for the importance of the knowledge of plasma physics for thermonuclear reactions. In this work we shall be concerned with fusion reactions solely from the view point of plasma physics. One concept which has been long in vogue is to attain thermonuclear reactions for plasma of relatively low density confined by magnetic field into toroidal or mirror configuration. A recent progress in this direction has 2 ) been the construction of tokamak for this purpose However, in recent years the invention of laser beams of high power has been a significant development following an entirely different principle where the nuclear fuel initially in solid state is plasmatized by irradiating with pulsed laser radially from all directions 3) Due to gasdynamic ablation it is conjectured that one can reach very high density and temperature which should be sufficient for the achievement of thermonuclear reactions.
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